Problem: Solve for $x$ and $y$ using elimination. ${-x-6y = -29}$ ${x-5y = -15}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-11y = -44$ $\dfrac{-11y}{{-11}} = \dfrac{-44}{{-11}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-x-6y = -29}\thinspace$ to find $x$ ${-x - 6}{(4)}{= -29}$ $-x-24 = -29$ $-x-24{+24} = -29{+24}$ $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ You can also plug ${y = 4}$ into $\thinspace {x-5y = -15}\thinspace$ and get the same answer for $x$ : ${x - 5}{(4)}{= -15}$ ${x = 5}$